00100	INTRODUCTION TO RUNNING GEOMED.
00200	
00300		This section  is  literally  an  operating  manual;  you  are
00400	supposed  to  be  operating  GEOMED as you read. I will tell you what
00500	keys to type and you will type them to see for yourself what happens;
00600	although  an  explaination  is  given  later  for  each  command, the
00700	complexity of individual commandS  tends  to  obscure  their  use  in
00800	sequences.
00900	
01000		The  system  copy  of  GEOMED is started by typing "R GEOMED"
01100	carriage return at a III  display  console.  GEOMED  will  display  a
01200	window  frame  and  type  an  asterisk  and  await  single  character
01300	commands.   Typing carriage returns will yield more asterisks showing
01400	that GEOMED is alive and listening.
01500	
01600	INSTANT CUBE.
01700	
01800		Type the character "∞" to get a drawing of a cube.
01900		Adjust the pots on the III so that the cube looks right.
02000	
02100	TRANSLATION.
02200	
02300		Type the character ":" to move the cube right (positive x axis).
02400		Type the character ";" to move the cube left (negative x axis).
02500		Type the character ")" to move the cube up (positive y axis).
02600		Type the character "(" to move the cube down (negtive y axis).
02700		Type the character "*" to move the cube nearer (positive z axis).
02800		Type the character "-" to move the cube away (negative z axis).
02900	
03000		Clearly these command characters are not mnemonics, they were chosen
03100		because they do not require the TOP key and are conviently grouped
03200		in pairs under one's right hand.
03300	
03400	STRENGTH OF TRANSLATION.
03500	
03600		The distance the cube is moved by a  translation  command  is
03700	called  the  strength  of  translation  or TDEL. The value of TDEL is
03800	displayed in the upper right corner of the screen  and  is  initially
03900	one foot. The strength of translation is halved by typing the command
04000	character "/" or doubled by typing "\".
04100	
04200	WORLD FRAME OF REFERENCE.
04300	
04400		The  direction  the  cube moved was with respect to the world
04500	frame of reference which is a right  handed  coordinate  system,  the
04600	initial  camera  is  positioned  looking down the Z axis at the world
04700	origin. The world origin will be in the center of the display  screen
04800	a  simulated sixteen feet away; and the positive world X axis will be
04900	to your right; and the positive world Y axis will be  up;  until  you
05000	move the camera.
     

00100	CONTROL, META, AND META-CONTROL.
00200	
00300		Notice that the Stanford A.I. keyboard has four "shift"  keys
00400	labeled  SHIFT, TOP, META & CONTROL. SHIFT only determines whether an
00500	alphabetic letters is upper or lower case; GEOMED converts lower case
00600	letters into upper so that the SHIFT key has no effect on GEOMED. The
00700	TOP key allows two ASCII character codes to be on each physical  key,
00800	this  doubling  up  on  the  physical keys is not important to GEOMED
00900	since "TOP-E" can always be referred to as "@".   Finally,  of  great
01000	importance, the CONTROL and META keys add two extra bits to the 7-bit
01100	ASCII code, so that a 9-bit character is  sent  to  GEOMED.  In  this
01200	manual  the  characters  "α",  "β"  and  "ε"  will  be used as prefix
01300	abbreviations  for  CONTROL,  META  and  META-CONTROL  keying  of   a
01400	character.  For  example,  the  "W"-command  is  four  way MIRV'ed as
01500	follows:
01600	
01700				W	"W"	make a world.
01800			CONTROL-W	"αW"	make a window.
01900			   META-W	"βW"	make a camera.
02000		   META-CONTROL-W	"εW"	make an image.
02100	
02200		Furthermore,   the   GEOMED   command   scanner  accepts  the
02300	characters "α", "β" and "ε" as prefix modifiers  that  will  add  the
02400	appropriate control and meta bits to the next character. The question
02500	mark character, explained immediately below, is the only other prefix
02600	modifier character.
02700	
02800	QUESTION MARK "?".
02900	
03000		Typing  the  question  mark  charcter  "?"  followed  by  any
03100	character  will type a one line reminder of what commands are invoked
03200	by that character.
     

00100	ROTATION.
00200	
00300		The  rotation  command  characters  are  the  same   as   for
00400	translation  except  you must hold the CONTROL key down or prefix the
00500	command with an "α". Try rotating the instant cube about  the  X-axis
00600	with  "α:".  The positive direction of rotation is counter-clockwise.
00700	The negative direction of rotation is clockwise.
00800	
00900	STRENGTH OF ROTATION.
01000	
01100		The  strength of rotation is named RDEL, the value of RDEL is
01200	displayed in three formats in the upper  right  hand  corner  of  the
01300	screen:  as  a  pi  fraction;  in  degrees,  minutes, seconds; and in
01400	radians. The initial value of RDEL is π/4, 45 degrees, 0.785 radians.
01500	Analogous  to  translation,  the  strenght  of  rotation is halved or
01600	doubled by "α/" and "α\" respectively.
01700	
01800	ROTATION DEFAULT.
01900	
02000		Since a sequence of rotations is quite common, there is a way
02100	to make the CTRL key be sticky. The  usual  euclidean  transformation
02200	default  is translation world frame; but after typing the "@" command
02300	character, the euclidean default is rotation world frame. Translation
02400	default  is  restored  by  typing  "!".  The  state  of the euclidean
02500	transformation default is displayed in the GEOMED status.
     

00100	DRAWING A CUBE.
00200	
00300		Starting  with  a  fresh  copy  of  GEOMED,  type the command
00400	letters in the second column to get the advertised results:
00500	
00600	1.	V	Vertex body creation.
00700	2.	:)	Position the vertex into the first quadrant.
00800	3.	S;;	Make an edge and vertex and move left.
00900	4.	S((	Edge vertex down.
01000	5.	S::	Edge vertex right.
01100	6.	J↑	Join the first and last vertices of the wire.
01200	7.	*	Push the face lamina away from you.
01300	8.	S	Sweep the square face into a very thin solid.
01400	9.	--↑	Move the new face towards you giving the cube
01500			its appropriate depth.
01600	10.	@/):!	Rotate the cube to a more familiar position.
01700	
01800		This example illustrates four commands that haven't been
01900	mentioned yet:
02000	
02100		"V"	Vertex Body Creation.
02200		"S"	Sweep.
02300		"J"	Join two old vertices with a new edge.
02400		"↑"	Pop the stack.
02500	
02600	These commands take their arguments from and leave their results in a
02700	push down stack of bodies, faces, edges and vertices. The contents of
02800	the stack is displayed on the left hand side of the III screen.
02900	
03000		The  "V"  command  takes  no  arguments and pushs a brand new
03100	body,  face  and  vertex  into  the  stack.  This  degenerate   point
03200	polyhedron  satisfies  the  Euler  equation  F-E+V=2, 1-0+1=2, and is
03300	always placed at the world origin.
03400	
03500		The first three sweep commands in the example, sweep a vertex
03600	polyhedron  into  a  wire polyhedron by adding a new vertex and a new
03700	edge; incidentally preserving  Euler's  equation  as  do  all  GEOMED
03800	commands. The wire-sweep takes a Vertex argument, and returns the new
03900	vertex. The new vertex has the same locus as the argument vertex.
04000	
04100		After three sides of a  square  have  been  formed,  the  "J"
04200	command  creates a new face and a new edge between the first and last
04300	vertex of the wire face. The wire-join case of the "J" command  takes
04400	a  vertex  argument  and identifies it as the end of a wire and knows
04500	enough to fetch the other end of that wire, as its second argument.
     

00100	STACK COMMANDS.
00200	
00300		↑	POP STACK.
00400		α↑	ROTATE STACK UP.
00500		 ↓	COPY PUSH STACK DOWN.
00600		α↓	ROTATE STACK DOWN.
00700	
00800		 ↔	SWAP 1ST AND 2ND ELEMENTS OF THE STACK.
00900		α↔	SWAP 1ST AND 3ND ELEMENTS OF THE STACK.
01000		β↔	SWAP 1ST AND LAST ELEMENTS OF THE STACK.
01100		ε↔	SWAP 2ND AND 3RD ELEMENTS OF THE STACK.
01200	
01300	LINK FOLLOWING COMMANDS.
01400	
01500		< >	FACE RING.
01600		≤ ≥	EDGE RING.
01700		∨ ∧	VERTEX RING.
01800	
     

00100	DRAWING A TORUS.
00200	
00300	1.	V:@		First Vertex.
00400	2.	E*E*E*		Seven more vertices.
00500		E*E*E*E*
00600	3.	J↑		Form Lamina.
00700	4.	!//:		Position the lamina.
00800	5.	@S)S)S)S)	Sweep the face around the Y-axis.
00900		S)S)S)S)
01000	6.	↓>G↑		Glue the ends of the torus together.
01100	
01200	
01300	
01400	EXERCISES.
01500	
01600		1. DRAW THE SOMA CUBES AS IN FIGURE.
01700		2. DRAW A JACK AS IN FIGURE.